Question

One Friday night, two large groups of people called Newport Taxi Service. The first group requested 1 sedan and 2 minivans, which can seat a total of 16 people. The second group asked for 2 sedans and 3 minivans, which can seat a total of 26 people. How many passengers can each type of taxi seat?

Answer 1

A sedan can seat 4 people, and a minivan can seat 6 people

Step-by-step explanation:

To get the number of seats, we need to solve two system of equatons that will be gotten from the given information

The first group: 1 sedan and 2 minivans, which can seat a total of 16 people

let the number of seats in the sedan = s

let the number of seats in the mini van = m

1(s) + 2(m) = 16

s + 2m = 16 .....(1)

The second group: 2 sedans and 3 minivans, which can seat a total of 26 people

2(s) + 3(m) = 26

2s + 3m = 26 ...(2)

combining both equations:

s + 2m = 16 .....(1)

2s + 3m = 26 ...(2)

Using elimination method:

To eliminate any of the variables, they must have same coefficient in both equations

To eliminate s, we will multiply equation (1) by 2

2(s) + 2(2m) = 2(16)

2s + 4m = 32 (1*)

now both equations have same coefficient for s:

2s + 4m = 32 ...(1*)

2s + 3m = 26 ...(2)

subtract equation (2) from (1*)

2s - 2s + 4m - 3m = 32 - 26

m = 6

substitute for m in any of the equations:

using equation 2: 2s + 3m = 26

2s + 3(6) = 26

2s + 18 = 26

2s = 26 - 18

2s = 8

divide both sides by 2:

2s/2 = 8/2

s = 4

A sedan can seat 4 people, and a minivan can seat 6 people